Silhouette in viewport while sculpting
Assign the object an emissive material the color you want. Set the world background color to something you like, if you like.

Switch the view mode of your window to'Material'. If you want the new background color too, you'll have switch to 'Rendered'. I find a pie menu (with gestures) helps speed up the switch.

If you want a new background color without rendering, you can change that in User Preferences 'Themes'. If you need a quick switch of background color too, that's scriptable... see this BSE answer.